# Math 126 Note to Students

Welcome to Math 126. This is the third quarter of an introductory course in calculus.

### What makes this course interesting?

The use of calculus and its consequences cuts across many disciplines, ranging from biology to business to engineering to the social sciences. At the risk of oversimplifying, calculus provides powerful tools to study "the rate of change." For example, we might want to study how fast a disease is spreading through a population, by studying the "number of diagnosed cases per day". We hope that seeing how calculus can be used to solve real world problems will be interesting. Many practical applications of calculus involve functions that depend on more than one variable. You will begin to learn about the geometry of curves and surfaces and get an introduction to differentiation and integration of functions two or more variables. This course also expands upon the idea of linear approximations learned in math 124. You will learn how to make better approximations and to estimate how good these approximations are.

### What makes this course difficult?

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The hardest thing about calculus is precalculus. The hardest
thing about precalculus is algebra.
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You all know from previous math classes how one course will build upon the next, and calculus is no exception. Math 126 will not only use material from precalculus and algebra, but it will use material you learned in Math 124 and Math 125.

Very few of you will go on to major in mathematics or computer science, but most of you will eventually see how calculus is applied in your chosen field of study. For this reason, we aim for ability to solve application problems using calculus. Some of the homework problems are quite lengthy and building up your "mathematical problem solving stamina" is just one of the aims of this course. If you have taken the Math 120 at UW, you know what this all means. If you have not, it means that a large number of "word problems" ("story problems") or "multi-step problems" are encountered in the course. This is one key place Math 126 will differ from a typical high school course. In addition, it is important to note that the ability to apply calculus requires more than computational skill; it requires conceptual understanding. As you work through the homework, you will find two general types of problems: calculation/skill problems and multi-step/word problems. A good rule of thumb is to work enough of the skill problems to become proficient, then spend the bulk of your time working on the longer multi-step problems.

### Five common misconceptions

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Misconception #1: Theory is irrelevant and the lectures should be
aimed just at showing you how to do the problems.
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The issue here is that we want you to be able to do ALL problems – not just particular kinds of problems – to which the methods of the course apply. For that level of command, the student must attain some conceptual understanding and develop judgment. Thus, a certain amount of theory is very relevant, indeed essential. A student who has been trained only to do certain kinds of problems has acquired very limited expertise.

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Misconception #2: The purpose of the classes and assignments is to
prepare the student for the exams.
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The real purpose of the classes and homework is to guide you in achieving the aspiration of the course: command of the material. If you have command of the material, you should do well on the exams.

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Misconception #3: It is the teacher's job to cover the material.
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As covering the material is the role of the textbook, and the textbook is to be read by the student, the instructor should be doing something else, something that helps the student grasp the material. The instructor's role is to guide the students in their learning: to reinforce the essential conceptual points of the subject, and to show their relation to the solving of problems.

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Misconception #4: Since you are supposed to be learning from
the book, there's no need to go to the lectures.
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The lectures, the reading, and the homework should combine to produce true comprehension of the material. For most students, reading a math text won't be easy. The lectures should serve to orient the student in learning the material.

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Misconception #5: Since I did well in math, even calculus, in a good
high school, I'll have no trouble with math at UW.
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There is a different standard at the college level. Students will have to put in more effort in order to get a good grade than in high school (or equivalently, to learn the material sufficiently well by college standards).

### How do I succeed?

Most people learn mathematics by doing mathematics. That is, you learn it by active participation; it is very unusual for someone to learn calculus by simply watching the instructor and TA perform. For this reason, the homework is THE heart of the course and more than anything else, study time is the key to success in Math 126. We advise an average of 15 hours of study per week, OUTSIDE class. Also, during the first week, the number of study hours will probably be even higher as you adjust to the viewpoint of the course and brush up on precalculus/algebra skills. In effect, this means that Math 126 will be roughly a 20 hour per week effort; the equivalent of a half-time job! This time commitment is in line with the University Handbook guidelines. In addition, it is much better to spread your studying evenly as possible across the week; cramming 15 hours of homework into the day before an assignment is due does not work. Pacing yourself, using a time schedule throughout the week, is a good way to insure success; this applies to any course at the UW, not just math.

### What is the course format?

On Monday, Wednesday and Friday, you will meet with the Instructor for the course in a class of size approximately 160; these classes are each 50 minutes long. On Tuesday and Thursday you will have a 50 minute section of about 40 students run by a TA. During these sections, you will take quizzes and exams, work in small groups on worksheets, and participate in question and answer sessions. The worksheets are designed to lead you through particular ideas related to this course. The TA for the course will circulate around the individual groups to insure everyone is progressing.

### What resources are available to help me succeed?

Calculus is a challenging course and the math department would like to see every one of you pass through with a positive experience. To help, a number of resources are available.

- Your instructor and TA will be accessible to help you during office hours, which will be announced early the first week of the term. If you are new to the university, you might have the false impression that professors are aloof and hard to approach. Our faculty and TA's make themselves very accessible to help their students and you should not be afraid to ask for advice or help.
- The math department operates a Math Study Center (MSC), located in B-14 of Communications. This facility is devoted to help students in our freshman math courses only. The center has extensive hours of operation that will be announced the first week of class. The MSC is staffed by advanced undergraduate and graduate students who can help you with difficulties as you work through the course. In addition, many faculty hold office hours there as well. One useful piece of advice: The MSC is often overcrowded the day before homework is due; this is another good reason to spread your study time out over the week.
- Some students use the MSC as a place to meet a small group of fellow students in the course and work through problems together. Explaining solutions to one another is often the best way to learn.
- A large amount of material is available on line (including old quizzes, midterms, finals and worksheets) at

- Some students additionally hire a tutor for private help; a list of tutors can be obtain at the Math Student Services Office, C-36 Padelford Hall.

Good Luck this quarter.